Finite-size scaling analysis of two-dimensional deformed Affleck-Kennedy-Lieb-Tasaki states

TL;DR

This paper uses tensor network methods to analyze phase transitions in two-dimensional deformed AKLT states, accurately determining critical points and exponents, and confirming the universality class of the transitions.

Contribution

It introduces a finite-size scaling analysis using tensor renormalization group methods to study phase transitions in 2D AKLT states, including the identification of critical points and exponents.

Findings

The AKLT-FM transition belongs to the 2D Ising universality class.

Critical points are accurately determined using crossing points of ratios.

The Berezinskii-Kosterlitz-Thouless transition is characterized by correlation ratio crossings.

Abstract

Using tensor network methods, we perform finite-size scaling analysis to study the parameter-induced phase transitions of two-dimensional deformed Affleck-Kennedy-Lieb-Tasaki states. We use higher-order tensor renormalization group method to evaluate the moments and the correlations. Then, the critical point and critical exponents are determined simultaneously by collapsing the data. Alternatively, the crossing points of the dimensionless ratios are used to determine the critical point, and the scaling at the critical point is used to determine the critical exponents. For the transition between the disordered AKLT phase and the ferromagnetic ordered phase, we demonstrate that both the critical point and the exponents can be determined accurately. Furthermore, the values of the exponents confirm that the AKLT-FM transition belongs to the 2D Ising universality class. We also investigate the Berezinskii-Kosterlitz-Thouless transition from the AKLT phase to the critical XY phase. In this case we show that the critical point can be located by the crossing point of the correlation ratio.